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• W2296451205 abstract "We have formulated the basic laws of electromagnetic theory in quaternion form. The formalism shows that Maxwell equations and Lorentz force are derivable from just one quaternion equation that only requires the Lorentz gauge. We proposed a quaternion form of the continuity equation from which we have derived the ordinary continuity equation. We introduce new transformations that produces a scalar wave and generalize the continuity equation to a set of three equations. These equations imply that both current and density are waves. Moreover, we have shown that the current can not cir- culate around a point emanating from it. Maxwell equations are invariant under these transformations. An electroscalar wave propagating with speed of light is derived upon requiring the invariance of the energy conservation equation under the new transforma- tions. The electroscalar wave function is found to be proportional to the electric field component along the charged particle motion. This scalar wave exists with or without considering the Lorentz gauge. We have shown that the electromagnetic fields travel with speed of light in the presence or absence of free charges. In this paper we write the Maxwell equations in quater- nion including the Lorentz force and the continuity equation. We have found that the Maxwell equations are derived from just one quaternion equation. The solution of these equations shows that the charge and current densities are waves trav- eling with speed of light. Generalizing the continuity equa- tion resulted in obtaining three equations defining the charge and current densities. Besides, there exists a set of transfor- mation that leave generalized continuity equation invariant. When these transformations are applied to the energy con- servation law an electroscalar wave propagating with speed of light is obtained. Thus, the quaternionic Maxwell equa- tion and continuity equation predict that there exist a scalar wave propagating with speed of light. This wave could pos- sibly arise due to vacuum fluctuation. Such a wave is not in- cluded in the Maxwell equations. Therefore, the existence of the electroscalar is a very essential integral part of Maxwell theory. Expressions of Lorentz force and the power deliv- ered to a charge particle are obtained from the quaternion Lo- rentz force. Moreover, the current and charge density are solutions of a wave equation travelling with speed of light. Further- more, we have shown that the electromagnetic field travels with speed of light in the presence and/or absence of charge. However, in Maxwell theory the electromagnetic field travels with speed of light only if there is no current (or free charge) in the medium. We have found here two more equations re- lating the charge and current that should supplement the fa- miliar continuity equation. These two equations are found to be compatible with Maxwell equations. Hence, Maxwell equations are found to be invariant under these new transfor- mations. This suggests that the extra two equations should be appended to Maxwell equations. Accordingly, we have found an electroscalar wave propagating at the speed of light. The time and space variation of this electroscalar wave in- duce a charge density and current density even in a source free. The electroscalar wave arises due to the invariance of the Maxwell equations under the new set of transformations. We have shown that such a scalar wave is purely electric and has no magnetic component. This is evident from the Poynting vector that has only two components, one along the particle motion and the other along the electric field direction. We re-" @default.
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• W2296451205 date "2009-04-01" @default.
• W2296451205 modified "2023-09-23" @default.
• W2296451205 title "On the Generalized Maxwell Equations and Their Prediction of Electroscalar Wave" @default.
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